Equation of a Straight Line

1
Equation of a Straight Line
2
Investigation
y 2x 1
x 2 4
y
Fill in table
Write points as coordinates
Draw a coordinates grid and plot points
Draw a line through points
Use your two coordinates to calculate gradient
From your diagram find where the line cuts the Y
axis
(the y intercept!)
3
Repeat for y 3x 2
x 2 4
y
Fill in table
Write points as coordinates
Draw a coordinates grid and plot points
Draw a line through points
Use your two coordinates to calculate gradient
From your diagram find where the line cuts the Y
axis
(the y intercept!)
y -2x 4
Also
y ½ x 3
4
m
Y Intercept
(0 , 1)
y 2x 1
2
(0 , -2)
y 3x 2
3
y -2x 4
-2
(0 , 4)
(0 , -3)
y ½ x 3
½
5

• Equation is related to
• Gradient
• Y intercept (cuts Y axis)

y
(0 ,)
x
6

• Equation Gradient Y Intercept
• Y 3x 5
• Y - ½ x 7

3
(0 , 5)
- ½
(0 , 7)
7

• Equation Gradient Y Intercept
• Y 3x 5
• Y - ½ x 7

3
(0 , 5)
- ½
(0 , 7)
8

• Equation Gradient Y Intercept
• Y 3x 5
• Y - ½ x 7
• Y 8x 5
• Y -6x 9

3
(0 , 5)
- ½
(0 , 7)
(0, -5)
8
(0, 9)
-6
9
Equation of a Straight Line

• Is in form
• y mx c
• Ex 1 y - ¾ x 2
• m - ¾ , y int (0 , 2)
• Ex 2 m 9, y int (0 , -8)
• y 9x - 8

gradient
Y intercept (0 ,?)
10
Write down gradient and Y intercept

• 1. y 2x 4
• 2. y ½ x -7
• 3. y -5x 6
• 4. y x 8
• 5. y 7x
• 6. y 6 2x (careful)
• 7. y 9 3x
• 8. y 7

11
Write down the equation

• m Y intercept
• 1. 5 (0 , 7)
• 2. -5 (0 , 5)
• 3. ¾ (0 , -6)
• 4. -5 (0 , -5)
• 5. 1 (0 , 4)
• 6. 8 (0 , 0)
• 7. 0 (0 , 9)

12
Calculating equation
y
Gradient?
Need 2 points
(1 , 2)
m 2 (-1) 1 - 0
m
(x2, y2)
c
3/1 3
x
(0 , -1)
y intercept
-1
(x1, y1)
Equation y 3x - 1
13
Calculating equation
y
(-2 , 3)
Gradient?
(x1, y1)
Need 2 points
(2 , 1)
m 1 3 2 (-2)
m
(x2, y2)
c
-2/4 - ½
x
y intercept
2
Equation y - ½ x 2
14
Special Cases

• (annoying lines!)

y
(0 , 4)
Horizontal lines
Y 0x 4
Y 4
m 0
x
15
Special Cases

• (really annoying!)

No y intercept!
y
Vertical lines
(2 , 4)
m 8
x
(2 , 0)
(2 , -2)
16
Special Cases

• (really annoying!)

No y intercept!
y
Vertical lines
(2 , 4)
m 8
x
(2 , 0)
(2 , -2)
Equation x 2
17
Annoying Lines Equations

• Horizontal Lines (m 0)
• are in form y ? (i.e no x)
• Vertical lines (m 8)
• are in form x ? (i.e no y)

y
Y 5
(0 , 5)
(7 , 0)
x
X 7